Impact Probability & Impactor Size

The raw probability of a particular NEO colliding with the Earth is easy to calculate mathematically. The cross-sectional area of the Earth is approximately one part in 2.2 billion of the area of a sphere surrounding the Sun with a radius of one AU. Any Earth crossing asteroid will cross the Earth's orbit twice per revolution; therefore, for any randomly orbiting body there is a 1.1 billion to one probability of collision. The gravitational attraction of the Earth, and the fact that most asteroids have orbits that are at moderate inclinations to the Earth's plane increase this probability to an estimated 100 million to one. There are, however, a number of other factors that make this calculation suspect. Indeed, the whole subject is very complex, and poorly understood at this time.

Sub-Critical Impactors (SCI) are objects that impacts with the surface of the Earth, or have an effect on that surface, that have diameters of less than 1 kilometre. In addition to asteroids and comets there is increasing evidence (Bailey and Emel-Yanenko, 1997) that there is a significant population of "dormant" comets occupying Halley type orbits. These objects will have low albedos, and will consequently pose a substantial problem for observational analysis.

Near Earth asteroids (NEAs) are main belt asteroids or fragments of main belt asteroids injected into Earth crossing orbits by gravitational perturbation or mutual collisions. Their lives can be ended by collision with a planet or the Sun, collision with another asteroid or by ejection from the solar system resulting from gravitational perturbation (probably by Jupiter). These processes result in expected NEO lifetimes of 10 to 100 Myr. To have maintained the near constant SCI impact flux since the end of the late bombardment era some 3 GYr ago, there must be some method by which the NEO population is constantly replenished to negate the effects of attrition. It is fairly certain that Jupiter plays a key role in the deflection of main belt asteroids and short period comets onto Earth crossing trajectories, and the estimates of inbound flux agree well with the calculated replenishment rates required.

The observational population census for Earth crossing objects is only complete for objects in the 8-kilometre diameter range (such as 1627 Ivor) or larger. The detection completeness for 1 kilometre range is estimated to be in the region of 12%. However, as pointed out by Rabinowitz et al in 1994, population estimates will also be limited by the completeness of the sample studied, which will be biased towards the most easily observed NEOs; the largest and brightest. Purely observational methods are therefore currently inadequate for an accurate estimate of sub-1 kilometre objects. There are, however, two methods by which estimates can be made. Populations can be estimated from extrapolation of the limited observational results and theory. These estimated populations, coupled with the calculated dynamical lifetimes of the target objects produce estimates of flux for specific size ranges (Bowell & Morrison). Alternatively, the integrated impact flux over the past 3 GYr can be determined empirically by analysing crater density and distribution on Lunar maria.

Bowell and Muinonen have derived a population for objects with diameters between 10 and 1000 metres of 2.6 x 108, which is in close agreement with the Spaceguard Report model. Both figures lie well within the estimated errors of both models.

NEO diameter estimation relies on knowledge of the likely albedos of the objects concerned. D. Rabinowitz et al used the same albedo range as found in main belt asteroids (McFadden et al 1989), and deduced size and population data consistent with the Shoemaker model.

The size-frequency distribution figures published by Shoemaker in 1983, and used in the Spaceguard Survey Report (Morrison 1994) are generally accepted within the scientific community. Their results are shown in Figure 18. More recent observations of small earth crossing objects reported by Rabinowitz (1993) and Rabinowitz et al (1993) have suggested a modest enhancement in the 10 metre size range, but these rarely penetrate the atmosphere, except in the case of iron meteoroids, so the Shoemaker figures retain their validity for the purposes of this paper. The limited observational data available is in agreement with the lunar cratering record to a significant degree of accuracy.

Precise predictions of the positions and orbits of bodies in the solar system have been made, using Newtonian principles, coupled where necessary with suitable relativistic modifications. Recent work has shown that over long periods of time small uncertainties in the orbit or the dynamic model eventually become significant, requiring regular monitoring of the discovered objects and continual updating of their orbits. Where necessary, their predicted trajectories can then be revised. This situation is particularly important for near-Earth objects that happen to pass close to a planet, in particular the Earth, and should be considered the rule for cometary objects, whose orbits are known to be subject to irregular non-gravitational perturbations due to outgassing, or effects due to the physical fragmentation of the body.

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